Why does my Asus Laptop u48e shut off?

The computer keeps shutting down right in the middle of anything that is running. Even when no programs are running. Seems as though a power supply problem, same if on battery, which is new and fully charged, or when connected to the AC power source. Asus says it is hard drive problem, but not 100% sure. Upon re-boot, comes on saying shutdown problem, and asks if safe mode or not? Sometimes runs for 10 minutes, sometimes hours until it shuts off. Tried setting the laptop on a cooling pad, but still shuts off.

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